The realization of topology, an abstract mathematical concept, in correlated electronic and magnetic systems has revolutionized the field of condensed matter physics and materials science [1]}. In a topological state, the bulk and the boundary may have entirely different properties. For example, in a quantum spin Hall state the bulk is insulating, whereas the edge can support helical transport modes. These novel topological states are robust against external perturbation such as an external magnetic field. In the bulk of the quantum Hall state, the topological number that governs the integer Hall conductance (called Chern number) provides a criterion to classify the different topological phases which otherwise cannot be related by a continuous mapping [2]}. A topological band theory has been developed to explain bulk-boundary correspondence between the edge and the bulk states [3]}.
